instance of each. In this example, we simplify three suchpaths:
1. to : T1; T3; S, which reduces to:
S1: (price*vol >= 1000000);
T4: [issue, price, vol] => [com=NYS(issue), cap=price*vol]
2. to reduces to:
S1: (price*vol >= 1000000);
T5: [issue, price, vol] => [com=NAS(issue), cap=price*vol]
3.: T3; S. This reduces to:
S1: (price*vol >= 1000000);
T6: [com, price, vol] => [com, cap=price*vol]
With this, each path from a publisher to a subscriber isof the form select followed by transform, as shown inFigure 3.
The selects can now be implemented by an efficientcontent-based routing system, and the transformsperformed before delivering to subscribers. Going onestep further, we can combine the individually derivedpaths back into a single I/S, which may be implemented asa content-based publish/subscribe system. These paths canthen be split by adding an additional select based onmessage source, then tagging the transforms with a source. Before an event is delivered to a subscriber, it istransformed based on the I/S to which the clientsubscribed and the source of the message. Taggedtransforms can be stored in a table for lookup andexecution before the system delivers a message to a client.New subscriptions coming into any of the subscriptionpoints () have their contentfilters modified based on the filter arcs out of the root intothese spaces using a simple application of the rewriterules.
4.2 Expanding State to Event Streams
Suppose a mobile client subscribes to the IBM eventsfrom the information space equivalent to the events in using the state[n, p], «n: p > maxP, curP¬ s 9 «n: p, p¬ s
[n, p], «n: p > maxP, curP¬ s9 «n: maxP, p¬ s
(These are the identical rules discussed in theillustration of collapse in Section 2, except that we areignoring the volume field v of events.)
Say that a number of events have been delivered todisconnects. Suppose that at this point, the state in«IBM: 160, 140¬. While the client is disconnected,a long series of events is published, arriving at a new state«IBM: 200, 120¬. The mobile client then reconnects to thesystem. If the system is able to exploit the knowledge of
the client’s interpretation of event sequences, it should beable to deliver just the two events [IBM, 200] and [IBM, 120]rather than the much longer sequence of published events.The following table shows the original events, thegenerated state, and the compressed set of deliveredevents.
disconnect:
reconnect:
Given a state space S, a start state s0 and a goal state gin S, and a collapse rule, the expansion problem is definedas the generation of the most economical sequence ofevents which, starting from s0, yields g. The expansionproblem can be converted into a shortest path graph searchproblem. We represent the states in S as vertices in agraph, and define each possible event transition as anedge. We then label these edges with a cost. For thepurpose of this paper, we will assume each event has unitcost 1. Figure 4 shows a fragment of the state transitiondiagram for the above example (but for just IBM events --thus, issue name has been left out of both events and
states).
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